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Mabrok, Mohamed A.; Kallapur, Abhijit G.; Petersen, Ian R.; Lanzon, Alexander (October 2014). "Generalizing
Negative Imaginary Systems Theory to Include Free Body Dynamics: Control of Highly Resonant Structures With Free Body Motion".
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1594:{\displaystyle {\begin{bmatrix}PA+A^{T}P&PB-A^{T}C^{T}\\B^{T}P-CA&-(CB+B^{T}C^{T})\end{bmatrix}}={\begin{bmatrix}-L^{T}L&-L^{T}W\\-W^{T}L&-W^{T}W\end{bmatrix}}\leq 0.}
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375:> 0 for all ω in (0, ∞). This means that a system is Negative imaginary if it is both stable and a nyquist plot will have a phase lag between for all ω > 0.
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Lanzon, Alexander; Petersen, Ian R. (May 2008). "Stability
Robustness of a Feedback Interconnection of Systems With Negative Imaginary Frequency Response".
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of the topic and provide significant coverage of it beyond a mere trivial mention. If notability cannot be shown, the article is likely to be
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This result comes from positive real theory after converting the negative imaginary system to a positive real system for analysis.
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1343:{\displaystyle P=P^{T}\geq 0,{\text{ }}W\in \mathbb {R} ^{m\times m},{\text{and }}L\in \mathbb {R} ^{m\times n}}
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theory was introduced by Lanzon and
Petersen in. A generalization of the theory was presented in In the
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1143:{\displaystyle {\begin{bmatrix}{\begin{array}{c|c}A&B\\\hline C&D\end{array}}\end{bmatrix}}}
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Petersen, Ian; Lanzon, Alexander (October 2010). "Feedback
Control of Negative-Imaginary Systems".
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305:(SISO) case, such systems are defined by considering the properties of the imaginary part of the
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For all positive frequencies, the nyquist diagram of the system response is between .
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G(jω) and require the system to have no poles in the right half plane and
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Please help to demonstrate the notability of the topic by citing
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822:{\textstyle K=\lim _{s\to j\omega _{0}}(s-j\omega _{0})jG(s)}
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may be too technical for most readers to understand
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368:{\displaystyle j(G(j\omega )-G(j\omega )^{\ast })}
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426:is NI if the following conditions are satisfied:
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704:{\displaystyle s=j\omega _{0},\omega _{0}>0}
8:
50:Learn how and when to remove these messages
1350:such that the following LMI is satisfied:
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268:Learn how and when to remove this message
100:Learn how and when to remove this message
84:, without removing the technical details.
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1033:These conditions can be summarized as:
1029:is Hermitian and positive semidefinite.
1718:IEEE Transactions on Automatic Control
1622:IEEE Transactions on Automatic Control
941:{\textstyle \lim _{s\to 0}s^{k}G(s)=0}
82:make it understandable to non-experts
7:
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1022:{\textstyle \lim _{s\to 0}s^{2}G(s)}
14:
1154:of the transfer function matrix
31:This article has multiple issues.
299:Negative imaginary (NI) systems
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181:may not meet Knowledge (XXG)'s
39:or discuss these issues on the
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518:{\displaystyle \omega \geq 0}
379:Negative Imaginary Definition
217:"Negative imaginary systems"
183:general notability guideline
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1245:and there exists a matrix
303:single-input single-output
190:reliable secondary sources
179:The topic of this article
1768:Frequency-domain analysis
1740:10.1109/TAC.2014.2325692
1074:Negative Imaginary Lemma
541:{\displaystyle j\omega }
396:transfer function matrix
1689:10.1109/MCS.2010.937676
1644:10.1109/TAC.2008.919567
1238:{\displaystyle D=D^{T}}
967:{\displaystyle k\geq 3}
489:{\displaystyle Re>0}
131:, as no other articles
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90:January 2016
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33:Please help
30:
1037:The system
194:independent
1607:References
1066:is stable.
525:such that
228:newspapers
202:redirected
146:; try the
133:link to it
36:improve it
1731:1305.1079
1680:1401.7745
1635:1401.7739
1586:≤
1562:−
1544:−
1524:−
1506:−
1449:−
1438:−
1398:−
1333:×
1320:∈
1313:and
1301:×
1288:∈
1271:≥
990:→
959:≥
903:→
793:ω
786:−
769:ω
762:→
687:ω
674:ω
638:≥
628:∗
620:ω
608:−
602:ω
536:ω
510:≥
507:ω
394:A square
358:∗
350:ω
338:−
332:ω
192:that are
136:. Please
42:talk page
1762:Category
1748:39372589
1697:27523861
1652:14390957
1183:. Then,
948:for all
499:For all
887:, then
242:scholar
206:deleted
76:Please
1746:
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1281:
1078:": -->
383:": -->
244:
237:
230:
223:
215:
198:merged
129:orphan
127:is an
1744:S2CID
1726:arXiv
1693:S2CID
1675:arXiv
1648:S2CID
1630:arXiv
1150:be a
249:JSTOR
235:books
204:, or
1089:Let
1080:edit
974:and
696:>
577:and
481:>
385:edit
221:news
1736:doi
1685:doi
1640:doi
983:lim
896:lim
832:If
755:lim
656:If
80:to
1764::
1742:.
1734:.
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